We have shown that the generally accepted DNA triple helix structure proposed by Arnott and Selsing (1976) is incorrect in important respects and have obtained a greatly improved model supported by clear experimental and molecular modeling evidence. In other recent work on triple helices we have shown that pyrimidine third strands must be parallel to the purine strand (Hoogsteen pairing). Proposed reverse Hoogsteen structures cannot be observed experimentally and are stereochemically unsatisfactory. With purine third strands (A to A, G to G) the opposite conclusion was reached. Triplexes can be formed in which two purine strands are antiparallel but cannot be formed if they are parallel. The human telomere sequence TTAGGGTTAGGG forms a single structure as a 12mer and a 24mer under defined conditions, in contrast to most of the sequences we and others have examined. By modeling we have obtained an attractive proposed structure in which all of the bases are paired. We have synthesized an analogous 9mer for attempted crystallization and NMR study. Though the DNA triple helices dC:dG:C+ are often referred to in the literature, we have found that they cannot be formed because of competing formation of the very stable poly dC acid helix. The same is true when dC20 or dC6 are used as potential third strands. We have prepared a Hoogsteen double helix with parallel strands using only natural nucleic acid bases. Infrared spectra in the conformationally sensitive region from 8000 to 900 cm-1 show that the backbone conformation of the duplex is virtually identical to that of the corresponding triple helix. We have also prepared a "parallel" DNA with reverse Watson-Crick pairing by attaching C2 "C clamps" to assure parallel structure. With certain sequences the structure remains parallel even without the terminal C's.